Explicit Perturbations to the Stabilizer $\tau = {\rm i}$ of Modular $A^\prime_5$ Symmetry and Leptonic CP Violation

TL;DR

This paper investigates how small deviations from the stabilizer point in a modular $A^\'_5$ symmetry model can induce significant leptonic CP violation, emphasizing the role of perturbations and renormalization-group effects.

Contribution

It constructs a neutrino mass model with modular $A^\'_5$ symmetry and analyzes how explicit perturbations near the stabilizer $ au = i$ lead to large CP violation.

Findings

Small deviations from the stabilizer induce large CP violation.

Renormalization-group effects are crucial for connecting high-energy predictions with low-energy data.

Explicit perturbations can explain observed leptonic CP violation.

Abstract

In a class of neutrino mass models with modular flavor symmetries, it has been observed that CP symmetry is preserved at the fixed point (or stabilizer) of the modulus parameter $\tau = {\rm i}$, whereas significant CP violation emerges within the neighbourhood of this stabilizer. In this paper, we first construct a viable model with the modular $A^\prime_5$ symmetry, and explore the phenomenological implications for lepton masses and flavor mixing. Then, we introduce explicit perturbations to the stabilizer at $\tau = {\rm i}$, and present both numerical and analytical results to understand why a small deviation from the stabilizer leads to large CP violation. As low-energy observables are very sensitive to the perturbations to model parameters, we further demonstrate that the renormalization-group running effects play an important role in confronting theoretical predictions at the high-energy scale with experimental measurements at the low-energy scale.